U.S. Democratic presidential candidate Hillary Clinton speaks to the media before boarding her campaign plane at the Westchester County airport in White Plains, New York, U.S. September 19, 2016. REUTERS/Carlos Barria

WASHINGTON/HIGH POINT, N.C. (Reuters) - Democratic presidential nominee Hillary Clinton consulted national security advisers on Tuesday after weekend bomb blasts renewed fears of domestic attacks, as Republican Donald Trump accused her of pushing policies that made the United States less safe.

The two rivals in the Nov. 8 election have been vying to portray themselves as the best equipped to protect the nation.

The domestic security issue returned to the forefront after a New York City bomb injured 29 people, a pipe bomb went off and unexploded bombs turned up in separate incidents in New Jersey, and a man stabbed 10 people at a Minnesota mall.

Clinton spoke by phone with former Defense Department official Michele Flournoy, former CIA deputy head Mike Morell and other advisers, her campaign said in an email.

"We can't lose our cool and start ranting and waving our arms," Clinton said on the call, according to her campaign in an apparent reference to Trump. "We shouldn't toss around extreme proposals that won't be effective and lose sight of who we are. That's what the terrorists are aiming for."

The call was supposed to be open to news media, but when reporters called in, they could not hear anything. Clinton's campaign provided notes to reporters afterward.

Clinton has called for better intelligence, new efforts to counter online recruiting of militants and smashing Islamic State strongholds in the Middle East.

She has said Trump's rhetoric against what he calls "radical Islamic terrorism" is helping Islamic State recruit more fighters.

At a rally in High Point, North Carolina, Trump countered by saying that Clinton, as Democratic President Barack Obama's first secretary of state from 2009 to 2013, backed policies that made the United States less safe.

"I'm much tougher than her on this horrible situation, but she goes around saying it's a recruiting tool," Trump said.

The New York businessman accused Clinton of supporting policies in Iraq and Syria that he said allowed Islamic State to take root.

Trump has pointed to the pullout of U.S. troops from Iraq in 2011 - which occurred after the Obama administration and Iraqi leaders could not agree on the withdrawal - and what he has characterized as a push for regime change in Syria. A U.S.-led coalition has conducted air strikes on Islamic State in Iraq and northern Syria.

Trump also criticized Clinton for supporting the entry of some Syrian refugees into the United States, reiterating his call for tougher vetting of people seeking admission. He has instead proposed safe zones for refugees, which he says Gulf states would fund.

"There's nothing like doing things with other people's money," Trump said at a rally later on Tuesday in Kenansville, North Carolina.

On Monday, U.S. authorities arrested Ahmad Khan Rahami following a shootout with police in Linden, New Jersey, in connection with the Saturday night bombing in Manhattan's Chelsea neighborhood. Rahami, 28, is a naturalized American citizen born in Afghanistan.

Law enforcement officials were also investigating the stabbings, also on Saturday night, at the St. Cloud, Minnesota, mall as "an act of terrorism. An off-duty policeman fatally shot the attacker, Dahir Adan, 20, whom an Islamic State news agency claimed as "a soldier" of the militant group. Reuters could not verify the claim.

Adan came from a Somali family that settled in the United States.

'GRAVY TRAIN'

At the Kenansville rally, Trump said he would dislodge a political establishment that he said ignored working people.

"They go to the same restaurants, they go to the same conferences, they have the same friends and connections, they write checks to the same think tanks and produce the same papers, it's a gravy train that never ends," Trump said.

Democrats, in turn, criticized Trump's business activities. U.S. Senate Democratic leader Harry Reid called the real estate developer a "fraud" in a speech on the Senate floor, pointing to his multiple bankruptcies and lawsuits.

Clinton's campaign repeated its call for Trump to release his tax returns after The Washington Post reported Trump's charitable foundation had spent thousands of dollars to settle lawsuits involving his businesses.